"Ndinofunga ndinogona kutaura zvakachengeteka kuti hapana anonzwisisa quantum mechanics." - Richard Feynman
Musoro we quantum computing wagara uchifadza vanyori vehunyanzvi uye vatori venhau. Kugona kwayo computational uye kuoma kwakapa iyo imwe mystical aura. Kazhinji, zvinyorwa zvinoratidzira uye infographics inotsanangura zvakadzama tarisiro dzakasiyana dzeindastiri iyi, nepo isingabatike pakushandisa kwayo kunoshanda: izvi zvinogona kutsausa muverengi asina kuterera.
Zvinyorwa zvesainzi zvakakurumbira zvinosiya tsananguro dze quantum masisitimu uye taura senge:
Yenguva dzose inogona kuva 1 kana 0, asi qubit inogona kuva 1 uye 0 panguva imwe chete.
Kana iwe uine rombo rakanaka (izvo zvandisina chokwadi nazvo), uchaudzwa kuti:
Iyo qubit iri mune superposition pakati pe "1" uye "0".
Hapana imwe yetsanangudzo idzi inoita seine musoro, sezvo tiri kuedza kugadzira quantum mechanical phenomenon tichishandisa mutauro wakagadzirwa munyika yechinyakare. Kuti utsanangure zvakajeka nheyo dze quantum computing, zvakakosha kushandisa mumwe mutauro - masvomhu.
Muchidzidzo ichi, ini ndichavhara maturusi emasvomhu anodiwa kuenzanisira uye kunzwisisa quantum computing masisitimu, pamwe nekuenzanisira uye kushandisa pfungwa ye quantum computing. Uyezve, ini ndichapa muenzaniso weiyo quantum algorithm uye ndikuudze kuti chakanakira chii pamusoro pechinyakare komputa.
Ndichaita zvandinogona kuti nditsanangure zvese izvi mumutauro wakajeka, asi ndichiri kutarisira kuti vaverengi vechinyorwa ichi vane nzwisiso yekutanga yemutsara algebra uye digital logic (linear algebra yakafukidzwa. , nezve digital logic - ).
Kutanga, ngatiendei pamusoro pemisimboti yedhijitari logic. Inobva pakushandiswa kwemagetsi emagetsi kuita masvomhu. Kuita kuti tsananguro yedu iwedzere kujeka, ngatirerutse mamiriro ewaya yemagetsi kuenda ku "1" kana "0", izvo zvinoenderana nematunhu "pa" kana "kudzima". Nekuronga ma transistors mune imwe nhevedzano, isu tichagadzira izvo zvinodaidzwa logic zvinhu zvinotora imwechete kana anopfuura ekuisa masaini kukosha uye ozvishandura kuita chiratidzo chekubuda zvichienderana nemimwe mitemo yeBoolean logic.
Common logic magedhi uye matafura avo enyika
Zvichienderana nemaketani ezvinhu zvakakosha zvakadaro, zvimwe zvakaoma zvinhu zvinogona kugadzirwa, uye zvichibva pamaketani ezvimwe zvinhu zvakaomarara, isu tinogona pakupedzisira, nehuwandu hukuru hwekubvisa, kutarisira kuwana analogue yepakati processor.
Sezvandambotaura, tinoda nzira yekumiririra digital logic masvomhu. Chekutanga, ngatitangei kusuma masvomhu echinyakare logic. Uchishandisa mutsara algebra, mabhiti emhando yepamusoro ane kukosha "1" uye "0" anogona kumiririrwa semakoramu maviri mavheji:
pane nhamba dziri kuruboshwe vector. Nekumiririra mabhiti edu nenzira iyi, tinogona kutevedzera mashandiro ane musoro pamabhiti tichishandisa vector shanduko. Ndokumbira utarise: kunyangwe kushandisa mabhiti maviri mumagedhi elogic kunogona kuita mashandiro akawanda (AND, KWETE, XOR, nezvimwewo), kana uchishandisa chidimbu chimwe chete, maoparesheni mana chete anogona kuitwa: kushandurwa kwekuzivikanwa, kuregeredza, kuverenga kweiyo nguva dzose "0" uye kuverenga kweiyo nguva dzose "1". Nekushandurwa kwekuzivikanwa, chidimbu chinoramba chisina kuchinjika, nekuramba, kukosha kudiki kunoshanduka kuenda kune zvakapesana (kubva "0" kuenda "1" kana kubva "1" kuenda "0"), uye kuverenga kweiyo nguva dzose "1" kana kuti “0” anoisa bhiti ku“1” kana “0” zvisinei neukoshi hwaro hwekare.
| kuzivikanzwa zvauri | Identity shanduko |
| Kukanganisa | Negation |
| Nguva dzose-0 | Kuverenga kwekugara "0" |
| Nguva dzose-1 | Kuverenga kwekugara "1" |
Zvichienderana nekumiririrwa kwedu kutsva kwezvishoma, zviri nyore kuita mashandiro pane inoenderana bit uchishandisa vector shanduko:
Tisati taenderera mberi, ngatitarisei pfungwa , izvo zvinongoreva kuti kuitira kuti uve nechokwadi chekudzoserwa kwechishandiso kana chinonzwisisika chinhu, zvinodikanwa kuti uone runyorwa rwemasaini ekuisa masaini zvichienderana neakabuda masaini uye mazita emashandiro anoshandiswa. Saka, tinogona kugumisa kuti kushandurwa kwekuzivikanwa uye kurambana kunodzokororwa, asi mashandiro ekuverenga maconstants "1" uye "0" haasi. Thanks to quantum mechanics, quantum makomputa anoshandisa chete anodzoreredzwa mashandiro, saka ndizvo zvatichatarisa pazviri. Tevere, tinoshandura zvisingadzoreki kuita zvinhu zvinodzoreredzwa kuti zvigone kushandiswa nekombuta yequantum.
Nekubatsirwa kwe mabhiti ega ega anogona kumiririrwa nemabhiti akawanda:
Zvino zvatine dzinenge dzese dzinodiwa masvomhu pfungwa, ngatienderere mberi kune yedu yekutanga quantum logic gedhi. Uyu ndiye mushandisi , kana kudzorwa Kwete (NOT), iyo yakakosha zvikuru mukudzoreredza uye quantum computing. Chinhu cheCNOT chinoshanda kune maviri mabhiti uye chinodzosa mabhiti maviri. Yekutanga bhiti inosarudzwa se "control" bit, uye yechipiri se "control" bit. Kana iyo control bit ikaiswa ku "1", iyo control bit inoshandura kukosha kwayo; Kana iyo control bit ikaiswa ku "0", iyo control bit haina kuchinjwa.
Uyu mushandisi anogona kumiririrwa seanotevera shanduko vector:
Kuratidza zvese zvatakavhara kusvika parizvino, ini ndinokuratidza mashandisiro echinhu cheCNOT pane akawanda mabhiti:
Kupfupisa izvo zvakatotaurwa: mumuenzaniso wekutanga tinoora |10⟩ muzvikamu zvechigadzirwa chayo uye shandisa iyo CNOT matrix kuwana hutsva hunoenderana mamiriro echigadzirwa; isu tobva tazvifungira ku |11 ⟩ zvinoenderana netafura ye CNOT tsika dzakapihwa kare.
Saka, isu takarangarira ese mitemo yemasvomhu iyo inotibatsira kunzwisisa echinyakare komputa uye akajairwa mabhiti, uye isu tinogona pakupedzisira kuenda kune yemazuva ano quantum computing uye qubits.
Kana iwe wakaverenga kusvika zvino, saka ndine nhau dzakanaka kwauri: qubits inogona kuratidzwa zviri nyore masvomhu. Kazhinji, kana classical bit (cbit) inogona kusetwa kuti |1⟩ kana |0⟩, iyo qubit ingori munzvimbo yepamusoro uye inogona kuva ese |0⟩ uye |1⟩ isati yayera. Mushure mekuyera, inodonha kuita |0⟩ kana |1⟩. Mune mamwe mazwi, qubit inogona kumiririrwa semusanganiswa wemutsara we |0⟩ uye |1⟩ zvinoenderana neformula pazasi:
apo a₀ и a₁ miririra, zvichiteerana, iwo amplitudes |0⟩ uye |1⟩. Izvi zvinogona kufungidzirwa se "quantum probabilities", inomiririra mukana wekuti qubit iwire mune imwe yenyika mushure mekuyerwa, sezvo mu quantum mechanics chinhu chiri mu superposition chinowira mune imwe yenyika mushure mekugadziriswa. Ngatiwedzere chirevo ichi uye titore zvinotevera:
Kurerutsa tsananguro yangu, iyi ndiyo inomiririra yandichashandisa muchinyorwa chino.
Kune iyi qubit, mukana wekudonha kune kukosha a₀ mushure mechiyero chakaenzana ne |a₀|², uye mukana wekupunzika kune kukosha a₁ yakaenzana ne |a₁|². Semuenzaniso, kune inotevera qubit:
mukana wekupunzika kuita "1" wakaenzana ne |1/ √2|², kana ½, kureva, 50/50.
Sezvo mu classical system mikana yese inofanirwa kuwedzera kusvika kune imwe (yekugovera kwakazara mukana), tinogona kugumisa kuti masikweya eiyo yakakwana kukosha kweamplitudes | 0⟩ uye |1⟩ inofanira kuwedzera kusvika kune imwe. Kubva pane ruzivo urwu tinogona kugadzira equation inotevera:
Kana iwe uchiziva trigonometry, uchaona kuti iyi equation inoenderana nePythagorean theorem (a²+b²=c²), kureva kuti, tinogona kumiririra zvinogoneka nyika dzequbit semapoinzi padenderedzwa reyuniti, zvinoti:
Vanonzwisisika vanoshanda uye zvinhu zvinoiswa kune qubits nenzira yakafanana nemamiriro ezvinhu ane classical bits - zvichibva pane matrix shanduko. Ese invertible matrix operators atakarangarira kusvika zvino, kunyanya CNOT, anogona kushandiswa kushanda nemaqubits. Vakadaro matrix vanoshanda vanokutendera kuti ushandise imwe neimwe yeamplitudes yequbit pasina kuyera nekuipunzika. Rega ndikupe muenzaniso wekushandisa negation operator pane qubit:
Tisati taenderera mberi, rega ndikuyeuchidze kuti amplitude values a₀ uye a₁ ndizvo chaizvo , saka mamiriro equbit anogona kunyatso kunyorwa pamativi matatu-dimensional unit sphere, inozivikanwawo se. :
Nekudaro, kuti tsananguro ireruke, tichazviganhurira pano kune nhamba chaidzo.
Zvinoita senge inguva yekukurukura zvimwe zvinhu zvine musoro izvo zvine musoro chete mumamiriro eiyo quantum computing.
Imwe yeanonyanya kukosha evashandisi ndeye "Hadamard element": inotora zvishoma mu "0" kana "1" mamiriro uye inoiisa mune yakakodzera superposition ine 50% mukana wekupunzika kuita "1" kana "0" mushure mekuyera.
Ziva kuti pane nhamba isina kunaka mudivi rekurudyi remushandisi weHadamard. Izvi zvinokonzerwa nekuti mhedzisiro yekushandisa mushandisi zvinoenderana nekukosha kwechiratidzo chekuisa: - |1⟩ kana |0⟩, uye saka kuverenga kunodzoserwa kumashure.
Imwe pfungwa yakakosha nezve chinhu cheHadamard kudzoreredzwa kwayo, zvichireva kuti inogona kutora qubit mune yakakodzera superposition uye ichishandura kuita | 0⟩ kana |1⟩.
Izvi zvakanyanya kukosha nekuti zvinotipa kugona kushandura kubva kune quantum state tisingatarise mamiriro equbit - uye, maererano, pasina kuiputsa. Nekudaro, isu tinokwanisa kugadzira quantum computing zvichibva pane deterministic pane probabilistic musimboti.
Quantum vanoshanda vane nhamba chaidzo chete ndivo vakapesana, saka tinogona kumiririra mhedzisiro yekushandisa mushandisi kune qubit seshanduko mukati meunit denderedzwa muchimiro chemuchina wehurumende:
Nokudaro, iyo qubit, iyo mamiriro ayo anoratidzwa mumufananidzo uri pamusoro, mushure mekushandisa kushandiswa kweHadamard, inoshandurwa kuva mamiriro anoratidzwa nemuseve unoenderana. Saizvozvo, isu tinokwanisa kuvaka mumwe muchina wehurumende unozoratidza shanduko yequbit tichishandisa mushandisi wekuramba sezvakaratidzwa pamusoro (inozivikanwawo sePauli negation operator, kana bit inversion), sezvakaratidzwa pasi apa:
Kuita mamwe mabasa akaomarara pane yedu qubit, tinogona kubatanidza akawanda maopareta kana kuisa zvinhu kakawanda. Muenzaniso we serial shanduko yakavakirwa pa zvinoita seizvi:
Ndokunge, kana tikatanga ne bit | 0 ⟩, shandisa zvishoma inversion, uyezve Hadamard oparesheni, ipapo imwe diki inversion, uye zvakare Hadamard oparesheni, inoteverwa neyekupedzisira bit inversion, tinopedzisira nevector yakapihwa nemberi. rutivi rworudyi rwecheni. Nekuisa mashini akasiyana ehurumende pamusoro peumwe neumwe, tinogona kutanga pa | 0⟩ uye titeedzere miseve ine mavara inoenderana neimwe yeshanduko kuti tinzwisise kuti zvese zvinoshanda sei.
Sezvo tasvika zvino, yave nguva yekufunga imwe yemhando dze quantum algorithms, iyo - - , uye ratidza mukana wayo pane yekare komputa. Zvakakosha kucherechedza kuti Deutsch-Jozsa algorithm inonyatso deterministic, kureva, inodzorera mhinduro chaiyo 100% yenguva (kusiyana nemamwe akawanda quantum algorithms zvichienderana netsanangudzo ye qubits).
Ngatimbofungidzira kuti une bhokisi dema rine basa / opareta pane imwe bhiti (rangarira - nekadiki, mana chete maoparesheni anogona kuitwa: kushandurwa kwekuzivikanwa, kuregeredza, kuongororwa kweiyo nguva dzose "0" uye kuongororwa kweiyo nguva dzose "1 "). Chii chaizvo basa rinoitwa mubhokisi? Iwe hauzive kuti ndeipi, asi iwe unogona kupfuura akawanda akasiyana ezvekukosha kukosha sezvaunoda uye kuongorora zvinobuda.
Mangani ekuisa uye zvinobuda zvaungada kumhanya nebhokisi dema kuti uone kuti nderipi basa riri kushandiswa? Funga pamusoro peizvi kwechipiri.
Panyaya yekombuta yekare, iwe unozofanirwa kuita 2 mibvunzo kuti uone basa rekushandisa. Semuenzaniso, kana iyo yekuisa "1" ichiburitsa "0" kubuda, zvinova pachena kuti kana basa rekuverenga risingaperi "0" kana basa rekuramba rinoshandiswa, mushure mezvo unozofanira kushandura kukosha kwechiratidzo chekuisa. ku "0" uye ona zvinoitika pakubuda.
Panyaya yekombuta yequantum, mibvunzo miviri ichadikanwa zvakare, sezvo iwe uchiri kuda maviri akasiyana maitiro ekuburitsa kuti unyatso kutsanangura basa rekushandisa kune kukosha kwekuisa. Nekudaro, kana iwe ukagadzirisa mubvunzo zvishoma, zvinozoitika kuti quantum makomputa ichine mukana wakakura: kana iwe waida kuziva kana basa riri kushandiswa rinogara riripo kana rakasiyana, quantum makomputa angave nemukana.
Iro basa rinoshandiswa mubhokisi rinoshanduka kana hunhu hwakasiyana hwechiratidzo chekuisa huchiburitsa mhedzisiro dzakasiyana pane zvinobuda (semuenzaniso, chiziviso shanduko uye bit inversion), uye kana kukosha kwekubuda kukasachinja zvisinei nekukosha kwekuisa, ipapo iyo basa rinogara riripo (somuenzaniso, kuverenga nguva dzose "1" kana kuverenga nguva dzose "0").
Uchishandisa quantum algorithm, unogona kuona kana basa riri mubhokisi dema rinogara kana kuchinjika zvichibva pamubvunzo mumwe chete. Asi tisati tatarisa maitiro ekuita izvi zvakadzama, tinoda kutsvaga nzira yekugadzira imwe neimwe yeaya mabasa pane quantum komputa. Sezvo chero ma quantum opareta achifanira kuchinjika, isu tinobva tatarisana nedambudziko: mabasa ekuverenga maconstindus "1" uye "0" haasi.
Mhinduro yakajairwa inoshandiswa muquantum computing ndeyekuwedzera imwe inobuda qubit inodzosera chero kukosha kwekuisa iyo basa rinogashira.
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Neiyi nzira, isu tinokwanisa kuona iyo yekuisa kukosha zvinoenderana chete neiyo inobuda kukosha, uye basa rinova invertible. Chimiro che quantum maseketi chinogadzira kudiwa kwekuwedzera bhiti rekuisa. Nekuda kwekuvandudza maopareta anoenderana, isu tichafunga kuti iyo yekuwedzera yekuisa qubit yakaiswa ku |0⟩.
Tichishandisa iyo yakafanana quantum yedunhu inomiririra iyo yatakamboshandisa, ngationei kuti chimwe nechimwe chezvinhu zvina (chiziviso shanduko, kuregeredza, kuongororwa kweanogara "0" uye kuongororwa kweanogara "1") anogona kuitwa uchishandisa quantum operators.
Semuenzaniso, iyi ndiyo nzira yaungaita nayo basa rekuverenga nguva dzose "0":
Kuverenga kweiyo nguva dzose "0":
Kuno hatichada maoperator zvachose. Yekutanga yekuisa qubit (yataifungidzira kuti |0⟩) inodzoka neukoshi hwakafanana, uye yechipiri kukosha kwekuisa inozvidzosa - semazuva ese.
Nebasa rekuverenga iyo nguva dzose "1" mamiriro acho akasiyana zvishoma:
Kuverenga kweiyo nguva dzose "1":
Sezvo isu takafunga kuti yekutanga yekuisa qubit inogara yakaiswa ku | 0⟩, mhedzisiro yekushandisa iyo bit inversion opareta ndeyekuti inogara ichiburitsa imwe pane inobuda. Uye semazuva ese, yechipiri qubit inopa kukosha kwayo pane inobuda.
Paunenge uchigadzira identity shanduko opareta, basa rinotanga kuve rakaoma. Heino maitiro ekuzviita:
Kufanana shanduko:
Chiratidzo chinoshandiswa pano chinoreva chinhu cheCNOT: mutsara wepamusoro unoreva bhiti rekudzora, uye mutsara wepasi unoreva bhiti rekudzora. Rega ndikuyeuchidze kuti kana uchishandisa CNOT opareta, kukosha kweiyo control bit inoshanduka kana iyo control bit yakaenzana |1⟩, asi inoramba isina kuchinjika kana iyo yekudzora bit yakaenzana |0⟩. Sezvo isu taifungidzira kuti kukosha kwemutsara wepamusoro nguva dzose kuenzana | 0 ⟩, kukosha kwayo kunogara kwakagoverwa kuzasi.
Isu tinoenderera nenzira yakafanana neyekuramba opareta:
Negation:
Isu tinongotenderedza bhiti pamagumo emutsara wekubuda.
Zvino zvatava nekunzwisisa kwekutanga kubva munzira, ngatitarisei mabhenefiti ehuwandu hwekombuta pamusoro pekombuta yechinyakare kana zvasvika pakuona kusimba kana kusiyanisa kwebasa rakavigwa mubhokisi dema uchishandisa mubvunzo mumwe chete.
Kuti ugadzirise dambudziko iri uchishandisa quantum computing muchikumbiro chimwe chete, zvinodikanwa kuti uise iyo qubits yekupinda mune superposition usati wapfuura iwo kubasa, sezvakaratidzwa pazasi:
Iyo Hadamard element inoiswazve kune mhedzisiro yebasa rekupwanya qubits kunze kwepamusoro uye kuita iyo algorithm deterministic. Isu tinotanga sisitimu muhurumende |00⟩ uye, nezvikonzero zvandichatsanangura munguva pfupi, tora mhedzisiro |11⟩ kana basa rakaiswa risingaperi. Kana basa riri mukati mebhokisi dema richichinja, saka mushure mekuyera sisitimu inodzosera mhedzisiro |01⟩.
Kuti tinzwisise zvasara zvechinyorwa, ngatitarisei mufananidzo wandaratidza pakutanga:
Nekushandisa bit inversion opareta uye wozoisa iyo Hadamard element kune ese ari maviri ekuisa kukosha akaenzana |0⟩, isu tinoona kuti anoshandurirwa mune imwecheteyo superposition ye|0⟩ uye |1⟩, sezvinotevera:
Uchishandisa muenzaniso wekupfuudza kukosha uku kune dema bhokisi basa, zviri nyore kuratidza kuti zvese zvinogara kukosha mabasa anobuda |11⟩.
Kuverenga kweiyo nguva dzose "0":
Saizvozvo, isu tinoona kuti basa rekuverenga risingaperi "1" rinogadzirawo | 11⟩ sekubuda, ndiko kuti:
Kuverenga kweiyo nguva dzose "1":
Ziva kuti zvinobuda zvichave |1⟩, kubvira -1² = 1.
Nemusimboti mumwechete, isu tinogona kuratidza kuti kana tichishandisa ese ari maviri akasiyana mabasa, isu tinogara tichiwana | 01⟩ pane zvakabuda (chero isu tikashandisa nzira imwechete), kunyangwe zvese zviri zvishoma zvakaoma.
Kufanana shanduko:
Sezvo CNOT iri maviri-qubit opareta, haigone kumiririrwa semuchina wehurumende wakapfava, uye saka zvinodikanwa kutsanangura masaini maviri anobuda zvichibva pane tensor chigadzirwa chezvese maviri ekuisa qubits uye kuwanda neiyo CNOT matrix sezvakatsanangurwa kare:
Neiyi nzira isu tinogona zvakare kusimbisa kuti kukosha kwekubuda |01⟩ inogamuchirwa kana basa rekuramba rakavanzwa mubhokisi dema:
Negation:
Nokudaro, tangoratidza mamiriro ezvinhu umo kombiyuta yehuwandu inonyatsoshanda kupfuura komputa yakajairika.
Chii chinotevera?
Ndinoti tigumire pano. Takatoita basa guru. Kana iwe wanzwisisa zvese zvandavhara, ndinofunga iwe ikozvino wava nekunzwisisa kwakanaka kweiyo yekutanga komputa komputa uye quantum logic, uye nei quantum algorithms inogona kunyatso shanda pane yechinyakare komputa mune mamwe mamiriro.
Tsananguro yangu haigone kunzi dhairekitori rakazara kune quantum computing uye algorithms - asi, sumo pfupi yemasvomhu uye notation, yakagadzirirwa kudzinga pfungwa dzevaverengi nezvechinyorwa chakaiswa neakakurumbira sainzi masosi (zvakanyanya, vazhinji havanyatso nzwisisa. mamiriro ezvinhu!). Ndakanga ndisina nguva yekubata-bata nyaya dzakawanda dzinokosha, dzakadai se , kuomarara kweamplitude kukosha | 0⟩ uye | 1⟩ uye kushanda kweakasiyana quantum logic zvinhu panguva yekushandurwa neBloch sphere.
Kana iwe uchida kuronga uye kuronga ruzivo rwako nezve quantum makomputa, nokuchimbidza Ndinokurudzira kuti uverenge Emma Strubel: kunyangwe nekuwanda kwemasvomhu mafomula, bhuku rino rinokurukura nezvehuwandu hwealgorithms mune zvakawanda zvakadzama.
Source: www.habr.com